Semiparametric Estimation Methods for Panel Count Data Using MonotoneB-Splines

Semiparametric partially linear varying coefficient models with panel count data

“…The conclusion is comparable with those given by Sun and Wei (2000), Zhang (2002), Wellner and Zhang (2007) and Lu et al (2009) among others, but the proposed model reveals more insight on how the effect of the number of initial tumors is moderated by the size of the largest initial tumor. In practice, one may specify (Z ; V ; W ) under a conceptual model according to research questions in which W is a possible moderator (effect modifier) of the association between the recurrent event process and covariate V .…”

“…. , p), the model reduces to linear regression model with panel count data, which has been well studied by Wellner and Zhang (2007) and Lu et al (2009), among others. When V r = 1 (r = 1, .…”

“…For example, Sun and Kalbfleisch (1995), Wellner and Zhang (2000), Zhang and Jamshidian (2003), Lu et al (2007), and Hu et al (2009a) studied nonparametric estimation for the mean function of the counting process with panel count data; Thall and Lachin (1988), Sun and Fang (2003), Zhang (2006), and Balakrishnan and Zhao (2009) proposed some nonparametric tests for the problem of nonparametric comparison of treatment groups based on panel count data. Sun and Wei (2000), Cheng and Wei (2000), Hu et al (2003), and Hua and Zhang (2012) discussed regression analysis of panel count data by the estimating equation-based approaches, while Zhang (2002), Wellner and Zhang (2007), and Lu et al (2009) presented more efficient inference procedures for joint estimation of parametric and nonparametric components in the proportional mean model by the likelihood-based approaches. In addition, Huang et al (2006) and Sun et al (2007) considered the analysis of panel count data with informative observation times.…”

A Nonparametric Regression Model for Panel Count Data Analysis

“…These papers demonstrated the benefits of spline-based estimators in analyzing panel count data. However, the effects of covariates on the mean function were assumed to be multiplicative in Lu, Zhang, and Huang (2009), which may be too restrictive in some applications.…”

“…We modify the proportional mean model for panel count data of Lu, Zhang, and Huang (2009) by incorporating non-linear covariate effects, and conduct a B-splines based functional analysis for the covariate effect using the pseudolikelihood approach of Zhang (2002) for its numerical advantages. Our method shows that the B-splines-based NPMPLEs of the baseline mean and the regression function are consistent and converge to the true corresponding functions at the rate of r/(1 + 2r), where r is the degree of smoothness of the baseline mean and the regression function.…”